Does the US government provide vaccines to US citizens working at the embassy in Bangkok?

@Kev ***

No. Especially now that the Thai government has "clarified" that expats will be vaccinated in Thailand for free as part of the vaccination program. Vaccinations under the program which involves locally produced AstraZeneca are expected to begin in June. They have promised that some means will be made available for expats to register for and receive the vaccination. It doesn't exist currently, although some expats have been able to register and even obtain appointments in June. Most expats have not been able to register via mor prom whether or not they had a pink ID card. I was able to register online in Phuket (which has a separate website for residents) by having a yellow house registration book which contains a Thai National ID number but have not been able to schedule an appointment yet.

It's probably the case that expats were never intended to use mor prom (or the Phuket alternative, for that matter). In any case, for the vast majority, it doesn't work. Whatever system expats are intended to use hasn't been fielded yet, but they have until June to get it up and running.